Social Dynamics

Reviewed by
Károly Takács
Corvinus University of Budapest, Institute of Sociology and Social Policy

Since Durkheim, social scientists realized that much of human development and welfare is due to efficient division of labor in the society. The problem of the division of labor is commonly compared with a permuted Stag Hunt game in which players need to specialize rather than to coordinate. These situations are part of the more general problem philosophers label as the problem of social contract. Skyrms highlights in this and his earlier work (e.g., Skyrms 1996 and 2004) that for modeling the problem of social contract, the use of Stag Hunt is more appropriate than the application of the Prisoner’s Dilemma. This should not demise all the important work on the Prisoner’s Dilemma. Rather, in line with the work of Skyrms, we should seek also more insights from versions of the Stag Hunt, which is the adequate model for a wide range of real-life social situations.

Well-established solutions to the problem of cooperation are kin selection (Hamilton 1964), repeated interaction (Axelrod 1984), and group selection (Bergstrom 2002). As Skyrms nicely illustrates, the repeated Prisoner’s Dilemma as well as the haystack model of group selection transfers the structure of the game into an easier – but still difficult – solution of the Stag Hunt, in which mutual cooperation is stable once it is established.

Once in the Stag Hunt, Skyrms concentrates on three mechanisms that can divert us from the hunting hare to hunting stag equilibrium. The solutions are built on various correlation and anti-correlation devices. First, spatial and network embeddedness offer a correlation device that allows for the clustering of stag hunters (local interaction) and for efficient imitation, learning, and reproduction that all take place in the spatial or network locality.

Second, these interactions change endogenously over time, such that network dynamics (due to partner selection) favors cooperation at the end. This is the conclusion form the work on “learning to network”, in which agents not only learn how to act, but also with whom to interact. Adaptive dynamics operate on both strategy and interaction structure, which quickly shifts the balance in favor of cliques of stag hunters, without any kind of rationality assumed.

Third, signaling and in particular signaling systems in which signals are not cheated and correctly interpreted can evolve and provide the solution in the Stag Hunt. Reinforcement learning helps to move coordination games to a signaling system in which signals are unambiguous (meaningful) with probability equal to one. This is the case with any kind of alarm signals for multiple predators (e.g., naming leopard, eagle, and snake to vervet monkeys: Cheney and Seyfarth 1990). Clear signals (e.g., territoriality in the Hawks and Doves game) could also change the outcome from a polymorphic equilibrium into a uniform population correlated equilibrium (e.g., play hawk if owner and dove if intruder). Furthermore, Skyrms claims that costless signals might also be of significant interest and can alter evolutionary equilibria, even in the Prisoner’s Dilemma case. Mutants can invade using the costless signal of a “secret handshake”; hence the state of all defection is not evolutionary stable anymore. This is not to say that cheap talk establishes cooperation in the Prisoner’s Dilemma, because they would be overwhelmed by defectors who fake the secret handshake. But with an arsenal of “secret handshakes” available, cooperators can stay ahead of defectors in the evolutionary arms race, and a high level of cooperation can be sustained.

In short, even a few initial cooperators can spread cooperation due to correlation (or anti-correlation) devices. The solution to the problem of social contract by correlation devices, however, has nothing to do with individual rationality. Mainstream economists and game theorists assume that everyone is rational in some sense and everyone knows this. There is only one type of individual, the rational one with the rational belief of rationality around him. This is very different in evolutionary game theory. As Skyrms writes: “One sort of story supposes that the decision makers involved reach equilibrium by an idealized reasoning process, which requires a great deal of common knowledge, godlike calculational powers, and perhaps allegiance to the recommendations of a particular theory of strategic interaction. Another kind of story — deriving from evolutionary biology — views game theoretic equilibria as fixed points of evolutionary adaptation, with none of the rational idealization of the first story.”

Only the latter can provide the solution to the problem of social contract for bacteria as well as for humans in a diverse world full of contingency. In fact, it is not just our species that divide labor efficiently or the only one that can be characterized by sophisticated rules that regulate the division of labor. The situations humans and bacteria face could even be of the same payoff structure. It is neither the payoff structure nor the set of alternatives that makes humans different from other species.

Beyond these elementary correlation devices that might also work well together and for any player without conscious decisions, humans have developed social institutions that serve to support the social contract even at a very large scale. Furthermore, Skyrms underlines that context and framing effects can make an enormous difference. He highlights that people can cooperate in the dictator game simply because they make mistakes in interpreting the task – but he does not emphasize that such mistakes could also ruin cooperation once it has been established.

We are social species, and we are very much influenced in our decisions and preferences by our friends and relevant others. This means more than learning from and imitating neighbours. It is wrong to attribute observed human behaviour in the dictator game entirely to framing. We do care about other non-related people. In the language of economics, their outcomes are part of our preferences.

The book is a collection of papers that were already published elsewhere. Now they are knit in a comprehensive volume with explanatory and summary notes. They cover “all sort of things” that are adaptive dynamics, including replicator dynamics, imitation, and reinforcement learning. The style is different from earlier volumes on similar topics (Skyrms 1996; 2004; 2010). Here, Skyrms first introduces the fundamental problems as well as the logic of the solutions in a way that is accessible to the general audience without any knowledge of game theory. The subsequent chapters, however, are more comfortably read by specialists and summarize the important rigorous work that Skyrms has done to justify the main messages. As expected for papers published in high-standard journals and edited volumes, he goes into the detail and provides the analytical formalization, the proofs, and evolutionary simulations in each chapter. Overall, the book collects important contributions of a leading scientist in evolutionary game theory and drives us to study correlation devices further as possible solutions for the problems of human cooperation and of the social contract with analytical and simulation tools.